Afraid of being Discriminated: Net Neutrality and Product Design

Transcription

1 Afraid of being Discriminated: Net Neutrality and Product Design Xingyi LIU February 14, 2013 Abstract We study the interaction between an Internet Service Provider and two Content Providers. The Content Providers choose their product designs from the most broad to the most niche, and the Internet Service Provider chooses a neutral or discriminatory network. We show that if the Internet Service Provider cannot commit to a discrimination policy, the Content Providers are biased to choose broader designs. This raises the concern that abandoning net neutrality regulation may have serious consequences on the content market. Key Words: Net Neutrality; Quality Discrimination; Product Design JEL Classification: D4, L80, L96 1 Introduction The development of Internet has brought up a massive amount of innovation in the products/contents that we can consume on the Internet. At the same time, the Internet is under various regulations, one of which is the net neutrality regulation. The notion of net neutrality was first brought up by Wu (2003), the central idea is that a maximally useful public information network aspires to treat all content, sites, and platforms equally. This originates from the public nature in the history of Internet. However, in 2005, the Federal Communication Commission (FCC) changed the classification of Internet transmission from telecommunication services to information services, and as a result, the Internet Service Providers are no longer subject to nondiscrimination regulation. Ever since, the debate on net neutrality has been a hot topic among lawyers, practitioners and economists. Economically, 1 the debate has been focused on the two-sided nature of Internet and how net neutrality would affect the investment incentives of Internet Service Providers(ISP) I thank Patrick Rey and Wilfried Sand-Zantman for their encouragement and useful comments. All remaining errors are mine. Toulouse School of Economics, GREMAQ, cristinliuxy@gmail.com 1 Schuett(2010) provides a thorough survey of the economic literatures on net neutrality. 1

2 and Content Providers(CP). 2 Among others, Economides and Tag (2012) and Hermalin and Katz (2007) analyzed the pricing of the platform(the ISP) in the two-sided market framework; Choi and Kim (2010), Kramer and Wiewiorra (2009), and Bourreau et al (2012) studied the investment incentives of ISPs and CPs in similar frameworks. However, our focus in this paper is different; we study the effect of net neutrality regulation on the choices of designs in the content market, rather than the pricing or investment behavior. To do this, we study the interaction between one Internet Service Provider(ISP) and two Content Providers(CPs). The ISP chooses a network structure, which can be either neutral or discriminatory. In a discriminatory network, the ISP favors one CP; while in a neutral network, both CPs are treated equally. More importantly, each CP can choose a design for his content. Our notion of designs builds on the concept of demand rotation by Johnson and Myatt (2006). The designs range from the most broad one which is acceptable for all consumers to the most niche one which is loved by some and hated by some others. Our central result shows that without net neutrality regulation, if the ISP lacks the ability to commit to a network structure, the CPs are inclined to design their products as broader ones. The reason underlying is simple: broader products are acceptable for more consumers, then favoring these products by giving them better connection quality can increase the demand more than favoring niche products which are attractive only to a small group of consumers. Therefore, each CP tends to choose a broader design so that he would not be discriminated against. This bias takes an extreme form in our linear example. The profit maximizing designs for the ISP and the social optimal designs are the most niche ones. If the ISP can commit to a network, he can induce the Content Providers to choose the optimal designs; however, if he cannot commit, such designs can never be achieved. The analysis in our paper underlines an important aspect that has been more or less ignored in the discussion of net neutrality, that is what impact such regulation would impose on the product designs in the content market, especially when the ISP lacks the ability to commit. The equilibrium has a simple prisoner s-dilemma structure. Everyone would be better-off with a niche product; however, everyone has incentive to design a slightly broader product. Enforcing net neutrality regulation endows the ISP the commitment power that he lacks, which can correct for the distortion of designs in the content market. Abandoning such regulation leaves some freedom for the choice of network, which has to be weighted against the distortion in the content market where the design is of significant importance. In this paper we proceed in the framework of net neutrality, however, we believe that the basic insight works in other environments also. As long as the owner of the network or other bottleneck resources can practice some form of discrimination, then lack of commitment may have a large impact on the upstream designs. For instance, the shelves in a supermarket differ in their locations, and the owner is likely to put broader products on those easy-to-find shelves. Thus if the owner lacks the ability to commit, the manufacturers are inclined to produce broader products. The paper is organized as follows: in section 2, we present the model and main results, 2 The ISPs invest in the network capacity, and the CPs invest in the qualities of their contents. 2

3 where a linear example is also shown; we briefly discuss some extensions and robustness of our results in section 3; and section 4 concludes. All omitted proofs are given in the appendix. 2 The Network/Design Model 2.1 The Model Consider a market with a representative consumer/user(u), a monopolistic Internet Service Provider(ISP), and two Content Providers(CP 1 and CP 2 ). The CPs distribute their products to the user through the network of the ISP. 3 Consumer The representative consumer has a utility function described as U = u(v 1, v 2 ; q 1, q 2 ) p where v i, i = 1, 2 is the match value between the consumer and the product of CP i. v i follows a distribution of F (s i, v i ), where s i is the design of CP i. 4 We assume that given designs s 1 and s 2, the realizations of v 1 and v 2 are independent. q i is the connection quality of v i, which is determined by how the ISP arranges the network. p is the price charged by the ISP. The reservation utility of the user is normalized to zero. Throughout this section, we consider the simplest case where the utility function takes the form U = max{v 1 + q 1, v 2 + q 2 } p so the consumer values connection quality in an additive way, and only consumes the product with a higher overall valuation. In other words, the two CPs compete for the consumer. Therefore, in this simple framework, we have the total demand for the service of the ISP equals the sum of the demands for the product of each CP, i.e. D = D 1 + D 2. Internet Service Provider The ISP charges a price p for the consumer. 5 More importantly, the ISP can arrange the network either as a neutral one or a discriminatory one, i.e. the ISP can choose an ω Ω = {neutral, favoring CP 1, favoring CP 2 }. Each CP is equally treated and attributed a connection quality of q in a neutral network; while in a discriminatory network, one CP is favored by the ISP and gets connection quality q > q, and the other CP is discriminated against and has connection quality q < q. 6 In this section, we assume that in a neutral network 3 We consider a situation where the network serves as a bottleneck resource for the market, so both the consumer and the CPs cannot bypass the ISP. 4 In the basic model, we consider the case where the match value is the only valuation that the user derives from the content. The content of CP i may also have an intrinsic value θ i that is independent from the match value; in this sense we consider the case of homogeneous CPs where θ 1 = θ 2 in the basic model. 5 We do not consider the case when the ISP also charge CPs for connection. Since the main focus in this paper is how the possibility of quality discrimination affects the design on the content market, but not how the ISP sets prices for the user and CPs. For more references on the price setting of the ISP, see the literatures on two-sided market. 6 In a discriminatory network, the ISP may auction out the priority or charge the favored CP in other manners, we consider this possibility in the following section. 3

4 q = 0; and in a discriminatory network, the connection quality is q = δ for the favored CP and q = δ for the disadvantage one, where δ [0, ]. 7 Content Providers Each CP chooses a design s S = [B, N] which ranges from the most broad(b) to the most niche(n). For each choice s, the realization of match value v follows a distribution F (s, v), with density function f(s, v) which is positive everywhere in the support [v s, v s ]. We assume that the CP is free to choose any design s S, and the marginal cost of production is zero. We follow Johnson and Myatt(2006) by assuming that different designs induce demand rotation. Definition 1. (Johnson and Myatt 2006): A local change of s leads to a rotation of F (s, v) if for some v s and each v (v s, v s ) v > v s F (s, v) s < 0 and v < v s F (s, v) s If this holds for all s, then {F (s, v)} is ordered by a sequence of rotations. The concept of demand rotation formalizes the idea that some designs induce a wider spread of consumer valuation than the others; or equivalently, some designs cater to a particular group of consumers and the others cater to a more general public. An increase in s leads to a clockwise rotation of the distribution function around the rotation point v s, so there are more consumers with high valuation, but also more consumers with low valuation. A higher s means a more niche product, and the bounds on s correspond to the most broad and most niche product. We focus on a class of rotation-ordered functions such that v s is decreasing in s. As proved in Johnson and Myatt(2006), with such rotation-ordered functions, the monopoly profit is quasi-convex in design s, and thus maximized at extreme designs. Assumption 1. {F (s, v)} is rotation-ordered in s and v s is decreasing in s. Profits For given designs s 1 and s 2, connection qualities q 1 and q 2, and price p, the profit for the ISP is π 0 = p D(s 1, s 2 ; q 1, q 2 ; p) where D(s 1, s 2 ; q 1, q 2 ; p) is the total demand for the service provided by the ISP. For the CPs, they do not directly charge the consumer; each CP i generates profit α i from one unit of demand for his product. 8 Then the profit for each CP i is 9 π i = α i D i (s 1, s 2 ; q 1, q 2 ; p) 7 We can also make other assumptions. For example, the consumer may value connection quality in a multiplicative way, so U = max{v 1 q 1, v 2 q 2 } p. In correspondence, we can alternatively assume q = 1 in the neutral network, and q = 1 + δ, q = 1 δ in the discriminatory network. However, this only changes the results quantitatively; the main results still hold. 8 We make this simplifying assumption that there is no difference in the profitability of the CPs; however, this does not affect our main results. We briefly discuss the more general case in section 4. 9 For example, this is the case when the CP generates profit from advertisements which positively depends on the demand for his product. The result in this paper is not sensitive to this assumption. We can readily make other assumptions on the profit of the CPs. For instance, the ISP and each CP i may share the profit that is generated from the demand for the product of CP i, which is the situation in the pay-tv market. > 0 4

5 where D i (s 1, s 2 ; q 1, q 2 ; p) is the demand for the product of CP i. Then in our additive utility assumption, for given designs s 1, s 2, connection qualities q 1, q 2, and price p, the total demand is given by D(s 1, s 2 ; q 1, q 2 ; p) = P rob(max{v 1 + q 1, v 2 + q 2 } p) (1) = 1 F (s 1, p q 1 )F (s 2, p q 2 ) and the demand for each CP i is D i (s i, s j ; q i, q j ; p) = p q i F (s j, v + q i q j )df (s i, v), j i (2) 2.2 The Benchmark Industry Profit Maximization For a benchmark, we consider the industry profit maximization designs and discrimination choice. For simplicity, we assume that α 1 = α 2 = α, and thus the industry profit becomes Then it is straightforward to show that Π = π 0 + π 1 + π 2 = (p + α)d(s 1, s 2 ; q 1, q 2 ; p) Proposition 1. Under Assumption 1, for any discrimination policy, the industry profit-maximizing designs for are extreme designs, (s m 1, s m 2 ) ES = {(B, B), (B, N), (N, B), (N, N)} Proof. The result follows immediately from proposition 1 of Johnson and Myatt(2006). First, it is obvious that F (s, v) is rotation-ordered implies that F (s 1, v)f (s 2, v) is rotation-ordered in both s 1 and s 2. Then with a given discrimination policy, for any designs s 1 < s 2, 10 suppose the price that maximizes Π is above the highest rotation point, i.e. p > v s 1, so that the industry profit maximizing quantity is below 1 F (s 1, v s 1 ) F (s 2, v s 1 ), then by the definition of rotation-ordering, an increase in either s 1 or s 2 would shift down F (s 1, v s 1 ) F (s 2, v s 1 ) since both v s i are decreasing in s i, and thus demand increases even the price is unchanged. Therefore a higher s i always leads to higher profit. Similarly, if p < v s 2, decreasing both s 1 and s 2 would increase demand when price is fixed. If v s 2 < p < v s 1, then increasing s 2 and decreasing s 1 at the same time would increase profit. Thus the profit maximizing designs must be extreme ones. 2.3 Equilibrium Analysis The Broad-Biased Design We consider both cases when the ISP can and cannot commit to a discriminatory policy. When the ISP cannot commit to a discriminatory policy, the CPs has to choose their designs before the ISP makes any arrangement to the network. Then the game proceeds as follows: Stage 1: The two CPs choose their designs s 1 and s 2 simultaneously; 10 Without loss of generality, we suppose s 1 < s 2, so that vs 1 > vs 2. 5

6 Stage 2: The ISP sets the price p and chooses whether to discriminate, i.e. chooses q 1 and q 2 ; Stage 3: The consumer observes both match values v 1, v 2, connection qualities q 1, q 2 and price p, then decides whether to connect to the service. We solve the game backwards. The consumer behavior is given by the demand function specified above: he only uses the content with higher overall value if it is greater than the price. For the ISP, two decisions have to be made: what price to charge for the consumer and whether to discriminate any of the Content Providers. We first see whether it is in the ISP s interest to introduce some discrimination when the two CPs choose the same design s. Recall that the profit function of the ISP is given by With neutral network, the profit of the ISP is Π = p (1 F (s 1, p q 1 )F (s 2, p q 2 )) (3) π N 0 = p(1 F (s, p)f (s, p)) If the ISP introduces a discrimination of δ, the profit becomes π 0 (δ) = p(1 F (s, p δ)f (s, p + δ)) we keep p fixed, take differentiation with respect to δ, then we have π 0 (δ) = p(f(s, p δ)f (s, p + δ) f(s, p + δ)f (s, p δ)) (4) Therefore, π 0(δ) = 0 at δ = 0; and π 0(δ) > 0 for any δ [0, ] if f F (s, p δ) > f (s, p + δ) F which is satisfied if F (s, v) is log-concave in v. Furthermore, take second order condition with respect to δ for a given p, we have 2 π 0 (δ) 2 = p(f(s, p δ)f(s, p + δ) f (s, p δ)f (s, p + δ) +f(s, p δ)f(s, p + δ) f (s, p + δ)f (s, p δ)) If F (s, v) is log-concave in v, it is easy to check that 2 Π(δ) 2 > 0 at δ = 0. Then we have Proposition 2. If F (s, v) is log-concave in v, and both CPs choose the same design s, then the ISP will choose a network with maximum discrimination δ =. 11 Given the price, introducing discrimination increases the demand for the favored CP; however it also decreases the demand for the discriminated CP. The log-concavity assumption ensures that the first effect dominates and the overall demand increases. When the choices of design differ between the two CPs, for instance, s 1, s 2 S, and s 1 < s 2, so CP 1 chooses a product that is broader, then we have the following result. 11 In this case, we assume that the ISP randomly favors either of the two CPs. 6

7 Proposition 3. When the designs of the two CPs are different, if F (s, v) is log-concave in s and v, the ISP will choose a network with maximum discrimination which favors the CP with broader design. Proof. See Appendix A. The reason why the ISP always favors the broader product is simple. For a given price, choosing a discriminatory network shifts down the distribution function of match value for the favored CP, and shifts up that for the discriminated one. The assumption on F (s, v) ensures that the downward-shift is larger when the broader product is favored and thus demand increases more. Simply speaking, improving the quality of a product that suits more consumers leads to a larger increase in demand than improving the quality of a product which is popular only among a small group of consumers. Then the problem for the ISP is simply to choose a price to maximize profit under a network with maximum discrimination which favors the broader product. That is to say, for any s 1 s 2, ISP s Problem: max p π 0 (s 1, s 2 ) = p (1 F (s 1, p )F (s 2, p + )) Now we turn to the choice of designs for the two Content Providers. The CPs have to make their design choices anticipating how they would be treated by the ISP ex post. Then it is clear from the above analysis that both CPs choose the most niche design cannot be an equilibrium. Moreover, the only possible symmetric equilibrium where both CPs choose the same design is where they both chooses the most broad design (B, B). Proposition 4. When the ISP cannot commit to a discrimination policy or can only commit to discrimination, if F (s, v) is log-concave in s and v, then any (s 1, s 2 ) (B, B) cannot be an equilibrium; in particular, (N, N) cannot be an equilibrium. Proof. It is easy to show that (N, N) cannot be an equilibrium. Suppose not, at s 1 = s 2 = N, the ISP will choose a discriminatory network which favors each CP with no more than probability 0.5. Then by choosing a design slightly broader s i = N ɛ, CP i induces a negligible change in the price charged by the ISP and the total demand of the consumer; however, this slightly change of design induces the ISP to favor CP i with probability 1, and thus CP i can get a larger share of the demand. Therefore this constitutes a profitable deviation for CP i. The same logic implies that any s 1 = s 2 B cannot be an equilibrium. The intuition for this results is simple. When the ISP cannot commit to how to treat the CPs, under the assumption that F (s, v) is log-concave in s and v, it is equivalent to say that the ISP commits to favor the broader product, thus each CP is afraid of being discriminated against if the other CP designs the product as a broader one; and therefore each CP tends to shift to broader designs. When the ISP can commit to a discriminatory policy, 12 the market unfolds as follows: 12 The case when the ISP can only commit to a discriminatory network but cannot commit on which CP to discriminate is different. Simply speaking, in this case the CPs still face unresolved uncertainty about the network. Thus in this sense, by commitment we mean all the uncertainty concerning the network structure is resolved. 7

8 Stage 0: The ISP announces a discriminatory policy, non-discrimination or discrimination; in case of discrimination, which CP is favored and which CP is discriminated against; Stage 1: The two CPs choose their designs s 1 and s 2 simultaneously; Stage 2: The ISP sets the price p; Stage 3: The consumer observes both match values v 1, v 2, connection qualities q 1, q 2 and price p, then decides whether to connect to the service. To proceeds, we make the following assumption, Assumption 2. D i > D j,for j i; and sign{ π i } = sign{ D i }. 13 The first part of Assumption 2 says that for each CP, keeping the price fixed, changing his product design has a larger impact on his own demand than on the demand of the other CP. 14 The second part of the Assumption says that the indirect effect on demand resulted from the induced change in price is dominated by the direct effect following a change in design. This assumption implies the following lemma, Lemma 1. If Assumption 2 is satisfied, then sign{ π 0 } = sign{ π i } for a given network structure. Proof. See Appendix B. Lemma 1 says that under Assumption 2, for a given network structure, if changing s i can increase/decrease the profit of the ISP, it also increases/decreases the profit of CP i. Then it immediately follows that, Proposition 5. Under Assumption 2, if the ISP can commit to a network, then in any a pure strategy equilibrium in the continuation design game, the CPs choose extreme designs, (s 1, s 2) ES = {(N, N), (B, N), (N, B), (B, B)} Proof. When the ISP commits to a network, given the design s j of CP j, the same intuition as proposition 1 applies for CP i. If p is above the rotation point, then increasing s i increases the profit for the ISP and thus also increases the profit for CP i ; on the other hand, if p is below the rotation point, decreasing s i increases the profit for both the ISP and CP i. If P is exactly at the rotation point, then either decreasing or increasing s i would increase the profit, keeping the price fixed. Thus the CPs always choose extreme designs. Corollary 1. If the ISP commits to a neutral network, a pure strategy equilibrium always exists. 13 A detailed assumption on the demand function is given in the appendix. 14 Similar assumptions are widely made in industry organization literatures. For example, in Bertrand competition with differentiated goods, we usually assume that the demand for a seller is more sensitive to his own price than to the rival s price. 8

9 Proof. Denote πn N (B, N) and πb N (B, N) as the profit for the niche and broad product under neutral network; denote π(n, N) and π(b, B) as the profit for each CP when they choose the same design. Since the two CPs are equally treated in a neutral network, we take (B, N) and (N, B) as one equilibrium. Then (N, N) is an equilibrium if π(n, N) πb N (B, N); (B, B) is an equilibrium if π(b, B) πn N (B, N). When neither (N, N) nor (B, B) is the equilibrium, we have π(n, N) < πb N (B, N) and π(b, B) < πn N (B, N), which implies that (B, N) is the equilibrium. We are particularly interested in the case where the efficient design is the most niche design in the sense that for any network structure, the profit for the ISP is higher when there are more niche designs; and given the design of the other CP, each CP gets higher profit with a more niche design. Specifically, denote Π(s i, s j ) as the maximum profit the ISP can earn if the designs are (s i, s j ); denote DN(s) ω and DB(s) ω as the demand for the niche product and the broad product under network ω given that the design of the other CP is s, where ω Ω = {neutral, favoring CP 1, favoring CP 2 }, we make the following assumption, Assumption 3. Π(N, N) > Π(B, N) > Π(B, B) and DN(s) ω > DB(s) ω for any ω Ω and s S. In this case, denote D(B, B) as the demand for each CP if both choose the most broad design and the ISP randomly favors one of them; denote D N (B, N) as the demand for the niche CP when the two CPs choose different designs and the ISP favors the broader CP. We have the following result, Corollary 2. Under Assumption 2 and 3, if F (s, v) is log-concave in both s and v, (a)when the ISP can commit to a network, (N, N) is the only equilibrium; (b)when the ISP lacks the ability to commit, there is no pure strategy equilibrium if D(B, B) < D N (B, N); (B, B) is the only equilibrium if D(B, B) > D N (B, N). Proof. See Appendix C. When the most niche design is the efficient choice for the CP, without uncertainty about the network, each CP can maximize his own profit without considering the design of the other CP. When such uncertainty prevails, on one hand, each CP intends to choose a more niche design so as to increase his profit; on the other hand, each CP is inclined to choose a broader design so as not to be discriminated against ex post. It is such concern that render some pure strategy non-sustainable in equilibrium. 15 The extreme consequence in this paper results from the assumptions we made on how designs affect the valuation for the product. The demandrotation system is taken for its convenience and transparency in analysis, but we believe that the result of broad-inclined design holds in more general environments when the network owner lacks the ability of commitment. 15 There may exist mixed strategy equilibria which is not in the scope of this paper. Nevertheless, more broad products would emerge in such equilibria and the broad-inclined result still holds. 9

10 2.4 A Linear Example We consider a linear example with the characteristic that the rotation point is fixed, which enables us to show explicitly how lack of commitment from the ISP could distort the product designs in the content market. Take the symmetric case θ 1 = θ 2 = θ; and the match value v s for a design s follows a uniform distribution on the interval [ s, s]. Thus, for each design s, the user valuation follows a uniform distribution on [θ s, θ + s], and the rotation point is θ for any design s. We assume that the design s S = [s, s], where s = s is the most broad design and the user valuation is more concentrated around θ; and s = s is the most niche design, the user may get very high or very low value. In this linear case, we have F (s, v) = v+s θ 2s f F (s, v) = 1 v + s θ and f(s, v) = 1, and thus 2s which is indeed decreasing in both s and v. Therefore, if s 1 < s 2, and the corresponding optimal price is such that f(s 1, v) is positive, the ISP prefers to give better connection to CP 1 ; explicitly, at such price, the demand in a network favoring CP 1 is D 1 = 1 p + s 1 δ θ p + s 2 + δ θ 2s 1 2s 2 the demand in a neutral network and a network favoring CP 2 is D N = 1 p + s 1 θ p + s 2 θ 2s 1 2s 2 Then it is easy to see that D 1 > D N and D 1 > D 2. and D 2 = 1 p + s 1 + δ θ p + s 2 δ θ 2s 1 2s 2 Therefore, if the two CPs choose the same design s, the ISP would choose a discriminatory network which randomly favors either one of the two CPs. The profit is then then the optimal price is Π = p(1 p + s θ δ 2s p + s θ + δ ) 2s p = (2s 2θ) + (2s 2θ) s 2 3(s θ δ)(s θ + δ) 3 Thus for a given δ, we have p > θ + δ if s > ŝ where ŝ = 2 θ if δ = 0; and ŝ increases with δ. We focus on the case where s ŝ, so that when 3 s 1 and s 2 are greater than ŝ, the optimal price is above the higher rotation point θ + δ; and thus the industry profit is increasing in s i and attains maximum at s i = s. Then we need to check if Assumption 2 is satisfied, which is equivalent to check that if increasing s i can increase the profit of the ISP, then it also increases the profit of CP i. In this linear example, when s ŝ, it is clear that the profit of the ISP is increasing in s i. Moreover, 10

11 increasing s i also increases the demand for CP i. Take CP 1 for example, if s 1 < s 2, the ISP chooses a network favoring CP 1, D 1 = θ+s1 p δ F (s 2, v + 2δ)dF (s 1, v) and D 2 = θ+s2 p+δ F (s 1, v 2δ)dF (s 2, v) Note that, for a given price p, we can see D 1 as a weighted summation of F (s 2, v), increasing s 1 leads to a clockwise rotation of F (s 1, v), this rotation shifts more weight to higher v, and thus more weight on higher F (s 2, v). Similarly, for D 2, it s a weighted summation over F (s 1, v), an increase in S 1 lowers the value of F (s 1, v) for each v, and thus lower the demand D 2. Thus, we must have D 1 s 1 > 0 > D 2 s 1 ; moreover, since D s 1 > 0, we have D 1 s 1 > D 2 s 1. Tedious algebra also shows that if D 1 s 1 > 0, then π 1 s 1 > 0, and vise versa. Hence, Assumption 2 is satisfied in the relevant range we consider. Therefore, in this linear example, the equilibrium must be extreme ones. Specifically, if the ISP can commit to a network, either neutral or discriminatory, since the profit for each CP increases with more niche designs, (s, s) is the only equilibrium. However, with limited commitment, (s, s) cannot be an equilibrium. And there exists a threshold s > s such that for s < s, D(s, s) > D s (s, s). equilibrium. So for s < s, (s, s) is the only Moreover in this linear example, it is easy to show that the social efficient designs and network are the most niche designs with a discriminatory network. Thus if the ISP is able to commit, the social optimal designs can be achieved; if not, the social optimal designs are never obtained. 3 Discussion and Extension 3.1 Bidding for Connection Quality In the model above, we assume that the ISP does not charge the CP for better connection. If the ISP can auction out the higher connection quality q, will this change the results? To see this, suppose s 1 < s 2, so CP 1 is favored by the ISP if there is no auction. For a given δ, denote D 1 i and p 1 as the demand for product CP i and price charged by ISP when CP 1 is favored; similarly D 2 i and p 2 as the demand and price when CP 2 is favored. Then the maximum amount CP i, (i = 1, 2) is willing to bid for high connection quality is b 1 = α(d 1 1 D 2 1) and b 2 = α(d 2 2 D 1 2) Thus, CP 2 cannot outbid CP 1 if D D 1 2 > D D 2 2, and this is indeed the case. f Proposition 6. If (s, v) is decreasing in both s and v, for given s F 1 < s 2, the demand is higher in a network which favors CP 1, and thus CP 1 can outbid CP 2 if the ISP can auction out the high connection quality. 11

12 Proof. See Appendix D. Therefore, even we allow the CPs to bid for better connection quality, the CP with the more niche design cannot outbid the broader one; and the tendency towards broader designs still exists. However, this result may change if there is a large difference in the profitabilities of CPs. Suppose CP i generates profit m i for each unit of demand D i, then the maximum amount CP i is willing to bid for high connection quality is b i = m i (Di i D j i ), j i For CP 2 to win the auction and the ISP chooses the network that favors CP 2, we need m 2 (D2 2 D2) 1 > m 1 (D1 1 D1) 2 (CP 2 wins) p 2 (D1 2 + D2) 2 + m 2 (D2 2 D2) 1 > p 1 (D1 1 + D2) 1 + m 1 (D1 1 D1) 2 (ISP favors CP 2 ) when m 2 is larger enough compared to m 1, CP 2 may outbid CP 1 and ISP may actually choose to discriminate the broader product. Thus, if there is systematic difference in the profitability of broad CP and niche CP, the CPs may instead tend to choose niche products Non-Competing Content Providers Up to now, we focus on the case when the two CPs compete for the user in the sense that the user only consumes the product with higher realized match value. In this subsection, we briefly discuss the case when the CPs do not directly compete for the user, i.e. the user can potentially consume both products. For simplicity, we assume that given the realized match value v 1,v 2 and price p, the utility of the consumer is U = max{v 1 + q 1, v 2 + q 2, v 1 + q 1 + v 2 + q 2 } p which means that the demand at given price is D(s 1, s 2 ; q 1, q 2 ; p) = P rob(max{v 1 + q 1, v 2 + q 2, v 1 + q 1 + v 2 + q 2 } > p) As in the previous section, we assume that in a neutral network q 1 = q 2 = 0; in a discriminatory network, the favored CP i has connection quality q i = δ, and the discriminated CP j has q j = δ. Suppose s 1 < s 2, we show that the ISP still favors the broader CP 1 under a slightly stronger assumption than the previous section. Proposition 7. When the content providers do not compete for the user, if f (s, v) is decreasing in both s and v, then the ISP prefers to choose a network with maximum discrimination which favors the broader product. And therefore, content providers are biased to choose broader designs. 16 For example, this may be the case if consumers with higher valuation for the product also create higher profit for the CP in the advertising market. In this case, the niche product catering to particular high valuation consumers may indeed obtain higher profit than a broader product. f 12

13 Proof. See Appendix E. The result of broad-inclined design in the previous section still holds when the two CPs do not directly compete for the user. The intuition remains the same: an increase in the connection quality of a broader product leads to a larger increase in demand than a niche product, since the valuation of the user is more concentrated around the center Asymmetric Content Providers In the previous section, we studied the case of symmetric content providers, i.e. the intrinsic value of CP i is the same for i = 1, 2; and the user valuations only differ in the match value. When the two CPs are asymmetric in the sense that one CP has a higher intrinsic value, the result of favoring the broader CP may be weakened. Denote the two CPs as CP L and CP H, CP i has an intrinsic value to the user θ i, we suppose θ L < θ H. The user s valuation for the product of CP i consists of three parts: the intrinsic value θ i, the match value v i, and the connection quality q i. Following the model of competing CPs in section 3, for a given price p, the demand for the service of the ISP becomes D = 1 F (s L, p θ L q L )F (s H, p θ H q H ) If s L = s H = s, the effect of favoring CP H in a discriminatory network δ on the demand is Thus D H = f(s, p δ θ H )F (s, p + δ θ L ) f(s, p + δ θ L )F (s, p δ θ H ) (5) sign DH = sign{ f(s, p δ θ H) F (s, p δ θ H ) f(s, p + δ θ L) F (s, p + δ θ L ) } Clearly, under the assumption that f is decreasing in v, D H > 0. Therefore, if the two F CPs have the same design, the ISP strictly prefer to favor the CP with higher intrinsic value; furthermore, even if CP H has a more niche design s H > s L, the ISP still prefers to favor CP H as long as θ H is large enough compared to θ L. The reason why the ISP would prefer favoring the more valuable CP to favoring the CP with broader design is simple. When the two CPs compete for the user, CP H has a larger chance of winning; and the price is closer to θ H. Thus by giving CP H a better connection quality, the ISP is able to charge a higher price for the user. Moreover, with asymmetric CPs, the high-value CP will generally chooses a broader design than the low-value one. The reason is quite obvious: when the two CPs compete for the user, the ISP would charge a price which is closer to θ H ; then the low-value CP L has to choose a more niche design so that there is a larger chance that the user will generate high match value from the low intrinsic value product. If CP L chooses a broad product, it may happen that 17 Note that in this simple framework, the choice of network structure of the ISP does not affect the utility of the user when he demands both contents, which simplifies the analysis here. However, as long as the impact of changing network structure has a larger impact on the user when he demands for one content only than when he demands for both contents, the result still holds. 13

14 the product never deliver high enough utility to the user in order to compete with CP H. For instance, in the linear example above, if θ L < θ H 2δ, the rotation point for CP L is always lower than the rotation point of CP H. Hence, if the two CPs choose different designs, it must be the high value CP H that chooses the broader product. This observation is consistent with the result of Bar-Isaac et al(2012), where they show that high valuation firms choose broad design and low valuation firms choose niche design in a search model. 3.4 Competing ISPs The results above are derived in the situation with a monopolistic ISP, and the results still hold under the presence of competition in the ISP market as long as consumers are not hugely differentiated in their tastes. In the simplest scenario, two ISPs locate at the end points of a Hotelling line, and consumers are uniformly distributed along the line. If consumers are only differentiated in their location, each ISP would still favor the CP with broader product, because any other network would reduce the utility a consumer would generate from connecting to his service. When consumers are highly differentiated in their tastes, for example, some consumers strongly prefer the product of CP 1 while the others strongly prefer that of CP 2, then each ISP would have incentive to differentiate himself from the other. In this case, we may have each ISP favors a different CP and each CP chooses his design without distortion. However, it seems implausible to see hugely differentiated consumer groups in reality. 4 Concluding Remarks on Net Neutrality In this paper we studied a simple model where the Internet Service Provider and content providers interact. The main result shows that if the ISP cannot commit to a network structure, the CPs are biased to choose broader designs. In some circumstances such as our linear example, such biases take an extreme form. The social optimal designs are achieved with commitment, while they are never achieved with limited commitment. The underlying reason is simple, with limited commitment, ex post the ISP prefers a network which favors the broader product; and thus each CP is inclined to design his product as broader ones in fear that he might be discriminated against ex post. This raises the concerns about the effect of net neutrality regulation if we take into account such impact it may have on the content market. Enforcing such regulation may reduce the biases on the designs of products, but it may also increase the biases on the network structure in case where a discriminatory network may be socially beneficial. Abandoning such regulation may not do much harm if the ISP is able to commit. However, if the ISP behaves opportunistically, the content markets may end up with many similar products, which the consumers like but don t love. Especially, this may be the case in emerging content markets, where content providers are less differentiated and there is a larger chance that the ISP would be opportunistic. Although this paper proceeds in the framework of net neutrality, we believe the intuition 14

15 that lack of commitment may have serious consequences on the upstream designs works in other environments also. For instance, a search engine is more likely to put a link which everybody may click at a higher click-through rate position rather than a link which only a few consumers might be interested in; a supermarket is likely to put a product that most consumers like at an easy-to-find shelf rather than a product that attracts only consumers with special tastes. The key insight is that if the downstream resource owner can potentially practice certain forms of discrimination, lack of commitment may seriously distort upstream investments. A Proof of Proposition 3 Proof. If s 1 < s 2, we first show the profit is higher when the ISP favors CP 1 than when he chooses a neutral network. The profit of the ISP is Π 1 (δ) = p(1 F (s 1, p δ)f (s 2, p + δ)) If δ = 0, the network is neutral; if δ > 0, the ISP favors CP 1. Fix p, take FOC w.r.t. δ, Π 1 (δ) = p(f(s 1, p δ)f (s 2, p + δ) f(s 2, p + δ)f (s 1, p δ)) sign{ Π 1(δ) } = sign{ f F (s 1, p δ) f F (s 2, p + δ)} If F (s, v) is log-concave in s and v, we have f F (s 1, p δ) > f F (s 2, p δ) > f F (s 2, p + δ) for all δ [0, ] Thus, we have Π 1(δ) > 0 for all δ [0, ]. Therefore, the ISP prefers a maximum discriminatory network which favors CP 1 to a neutral network. Then we need to show that a discriminatory network favoring CP 1 is preferred to a network favoring CP 2. It suffices to show that for a given p and δ, which is equivalent to which in turn is satisfied if F (s 1,x) F (s 2,x) F (s 1, p δ)f (s 2, p + δ) < F (s 1, p + δ)f (s 2, p δ) F (s 1, p δ) F (s 2, p δ) < F (s 1, p + δ) F (s 2, p + δ) is increasing in x, sign{ F (s 1,x) F (s 2,x) x } = sign{ f F (s 1, x) f F (s 2, x)} since F (s, v) is log-concave in s, we have f F (s 1, x) > f F (s 2, x). Thus, favoring CP 1 is better for the ISP than favoring CP 2. 15

16 B Details of Assumption 2 Assumption 2 can be obtained from a series of assumptions on the demand function D(s 1, s 2 ; p) and D i (s 1, s 2 ; p). (2.1) 2 D P 2 0 and D p > p 2 D p 2 for any p; (2.2) D i/ D i 1 2 D/ p D j/ ; / p 2 2 D/ p 2 D j / p We need to show that the above two conditions imply that sign{ π i } = sign{ D i }. First, we have then what we need to show is simply π i = α[ D i + D i p ] p D i D i p p The profit maximization problem for the ISP gives us the following first order condition D(s 1, s 2 ; p) + p(s 1, s 2 ) D(s 1, s 2 ; p) p(s 1, s 2 ) = 0 and thus we have Thus we need to show that From (2.1) we have p = D + p 2 D p 2 D + p 2 D p D + p 2 D p 2 D + p 2 D p p 2 p 2 D i D i p D + p 2 D p 2 D + p 2 D p p 2 D + p 2 D p + p 2 D D + p 2 D p D + 2p 2 D p p 2 p p 2 2 D The right hand side of the above equation is smaller than D i if D i p which is implied by (2.2), since D j + p 2 D p D j + 2p 2 D p D j + p 2 D p D j p + 2p 2 D p p 2 2 D p 2 D p 2 D i D i p D i D i p D i + D j + p 2 D p D i + D j + 2p 2 D p p p 2 16

17 C Proof of Lemma 1 Proof. It suffices to show that sign{ π 0 } = sign{ D i }. First, we have Envelop theorem immediately implies that π 0 (s i, s j ) = p(s i, s j )D(s i, s j ; q i, q j ; p(s i, s j )) π 0 = p D = p( D i + D j ) From assumption 2, D i > D j If Π Similarly, if Π > 0, then either D i,for j i. > D j < 0, we must have D i < 0. > 0 or D i > 0 > D j. So we must have D i > 0. D Proof of Corollary 2 Proof. In the commitment case, for any given network, DN(s) ω > DB(s) ω for any ω Ω and s S implies that N is a dominant strategy for each CP, and thus (N, N) is the only equilibrium. Without commitment, proposition 5 shows that (N, N) cannot be an equilibrium. For (B, N), the content provider B is favored by the ISP; then by choosing a design B such that B = N ɛ, this CP induces no change in the network but can attain strictly higher profit. For (B, B), each CP is favored by the ISP with the same probability; deviating to N means that this CP will be discriminated against for sure. Thus if D(B, B) < D N (B, N), such deviation is profitable, and no pure strategy equilibrium exists; on the contrary, if D(B, B) > D N (B, N), there is no profitable deviation and (B, B) constitutes the only equilibrium. E Proof of Proposition 6 Proof. Given s 1 and s 2, write the profit function as Π = p(1 F (s 1, p δ)f (s 2, p + δ)) where positive δ means that the network favors CP 1, δ = 0 in a neutral network, and in a network favoring CP 2 we have δ < 0. Envelop theorem implies that Π(δ) = p D(δ) where D(δ) = 1 F (s 1, p δ)f (s 2, p + δ), under the assumption that F (s, v) is log-concave in s and v, it is straightforward to show that Π(δ) = p D(δ) so the demand is higher in a network which favors the broader product CP 1. > 0 17

18 F Proof of Proposition 7 Proof. First, we show that if f(s, v) is log-concave in s and v, then F (s, v) is also log-concave in s and v. And therefore the condition in the proposition is stronger than that in the main model. Bagnoli and Bergstrom (2005) shows that if the p.d.f f(x) is log-concave, then the c.d.f. F (x) is also log-concave, which proves the log-concave in v part. If f(s, v) is log-concave in s, then it is easy to show that f(s 1,v) f(s 2,v) is increasing in v for s 1 < s 2. Moreover, we have f(s 1, v) F (s 1, v) f(s 2, v) F (s 2, v) = v (f(s 1, v)f(s 2, x) f(s 2, v)f(s 1, x))dx F (s 1, v)f (s 2, v) since f(s 1,v) f(s 2,v) > f(s 1,x) f(s 2,x) for any x < v, we must have f(s 1,v) F (s 1,v) > f(s 2,v) F (s 2,v). For a given price p, the user will connect to the services in a neutral network if either v 1 > p, or v 2 > p or v 1 + v 2 > p; in a discriminatory network which favors CP 1, the user connects if either v 1 + δ > p, or v 2 δ > p or v 1 + v 2 > p. Hence, if the ISP switches from neutral network to the discriminatory network favoring CP 1, the change in demand is D 1 (δ) = p p δ F (s 2, p x)df (s 1, x) p+δ p F (s 1, p x)df (s 2, x) Clearly, D 1 (δ) = 0 for δ = 0; then the ISP prefers a network favoring CP 1 to a neutral network if we have D 1 (δ) then it is easy to show that and = F (s 2, δ)f(s 1, p δ) F (s 1, δ)f(s 2, p + δ) > 0 sign{ D1 (δ) } = sign{ f(s 1, p δ) F (s 1, δ) f(s 2, p + δ) } F (s 2, δ) f(s 1, p δ) F (s 1, δ) > f(s 1, p + δ) F (s 1, δ) f(s 1, p + δ) F (s 1, δ) > f(s 2, p + δ) F (s 2, δ) hence D1 (δ) > 0 for all δ, so the ISP prefers a maximum discriminatory network favoring CP 1 to a neutral network. Next we show that favoring CP 1 is preferred to favoring CP 2. When the ISP favors CP 2, similarly we have Therefore, we have D 2 (δ) = p p δ D 1 (δ) D 2 (δ) = F (s 1, p x)df (s 2, x) p+δ p δ p+δ p F (s 2, p x)df (s 1, x) (f(s 1, x)f (s 2, p x) f(s 2, x)f (s 1, p x))dx Then as long as δ is small enough(δ < p δ), we must have D 1 (δ) > D 2 (δ) for all δ. So the ISP always prefers to favor CP 1 rather than CP 2. 18

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